Basic classifiers of formal classification theory of technical systems: hierarchies, vectors and matrices, bands

The article considers the importance of a technical system among other technical systems in order to ensure its functioning and development, to classify objects, subjects, processes of the technical and related systems. Previously, the author presented the basics of the formal classification theory. This article describes the basic classifiers and operations with them. Three types of basic classifications are identified: discrete hierarchical, discrete matrix and continuous band classifications. For them the concept, structure, dimension, basic operations (addition, multiplication, equality) are defined. In the hierarchy, the classification attributes can be sorted by subordination, when the classification attributes of the lower levels of the hierarchy detail the features of higher levels. The dimension of the hierarchical classification is the number of levels of classification features. Matrix classifications (including vector and super-matrix) are used when the classification attributes are equal and their values are discrete. Band classifications are similar in structure to matrix classifications, but the value of the classification attribute is the interval of numbers, for which the lower and upper boundaries are determined. The dimension of the matrix and band classifications is equal to the number of non-subordinate classification attributes. For all classifications, multiplication is equivalent to the introduction of new classification attributes, addition is the introduction of new values of already existing classification attributes. A unified approach to various types of classifications makes it possible to plan the structure of classifications of specific technical systems, taking into account the properties of characteristic parameters.